Undated (AP) _ Homeless people who wanted shelter from a severe winter storm found it last week, and in some cities they had their choice of beds in facilities which drew surprisingly few customers.

The Dallas Life Foundation has more than 900 beds available, but only about 400 were filled when freezing rain, ice and snow struck Wednesday.

''All I know is they just didn't show up,'' director Ray Bailey said.

In Salt Lake City, however, Traveler's Aid squeezed nearly 400 people in shelters which usually accommodate no more than 250.

''We are already at capacity,'' spokeswoman Priscilla Solarz said. ''But we have a policy that we do not put anyone on the streets. As long as we can find a few inches of space, we keep taking them.''

Meanwhile, Solarz said, Traveler's Aid in Salt Lake City is out of money and waiting for an overdue check for $17,000 from a federal program.

''We don't even have enough to cover the payroll,'' she said, adding that it costs about $30,000 a month to run the three city shelter sites.

''People are packing in here and they're staying longer,'' said Marilyn Schaaub, secretary of the Union Gospel in Duluth, Minn., where temperatures fell far below zero. ''It's too cold for anyone to leave.''

The Nashville Union Rescue Mission, which has an annual budget of slightly more than $1 million, fed an additional 200 people daily since the cold front hit Tennessee.

The mission feeds an average of 1,200 people a day, director Carl Resener said. By mid-week, that number had jumped to more than 1,400, he said.

The mission, which turns away no one needing food, clothing or shelter, provides beds for 500 people, and a number of churches take in an additional 50 people, he said. The mission also pays for low-cost motel rooms.

''I'll take them into my house if I have to,'' Resener said.

Gov. Edward D. DiPrete ordered emergency shelters opened in Rhode Island as temperatures dove into single digits last week and all 250 beds at existing shelters were full, but some of the emergency shelters had no customers.

Linda Barden, director of the Interim House shelter in Providence, R.I., said many homeless people probably did not hear the state's radio or television announcements.

Because of freezing temperatures in the nation's capital, the ground floor of City Hall was opened as an emergency shelter.

Private and city shelters, estimated to have as many as 2,500 beds, have been bulging in recent weeks. District Council Chairman David Clarke said he had been at one shelter that was serving almost double its capacity.

Though Dallas' emergency shelters were hardly strained last week, Texas does have a significant homeless population.

In 1987, 32 Salvation Army shelters around the state served 191,500 transients, up 15 percent from 1986, said Ron Carr, spokesman for the Salvation Army in Texas.

At best, says Stanley Burnham, director of administration for the Texas Department of Commerce, the state will receive $68 per person under the federal Homeless Assistance Act to assist the estimated 200,000 homeless.

Los Angeles' four emergency shelters harbored 3,500 homeless people while they were open during cold spells from Dec. 13 to Dec. 18 and again from Christmas Eve to Jan. 3, said Dee Dee Myers, a spokeswoman for Mayor Tom Bradley.

The Union Rescue Mission in Los Angeles already shelters 800 people a night, 460 more than can be accommodated on cots, and the mission opened a cellar with room for 50 more during the cold spell, said John Dickson, director of development. Men and women sleep on chairs, in the cellar, the chapel and elsewhere.

San Francisco officials say there isn't enough money for the homeless, but they're living within a $7.5 million allocation for this fiscal year despite unusually cold 30-degree weather last month.

''This has been a very cold winter for us, but we haven't seen any substantial increase in the demand for rooms,'' Judith Schutzman, director of administrative services for city's Social Services Department, said Thursday.

The city funds four privately run shelters with a total of 400 beds and also provides about 2,800 hotel rooms each night. ''Two or three nights a month, people are turned away,'' Schutzman said.

The recent storm added to the burden on 175 shelters in Philadelphia. About 4,500 people needed shelter last year, but officials at the city's Adult Services department say the number is now up to 6,600.

''There's a great strain on the system compounded by the severe cold weather,'' said Michael R. Phillips, deputy commissioner for Adult Services.

Between Thursday and Friday morning, 800 people had sought shelter at the city's emergency facilities and 31 were removed from the street and taken to city buildings, Phillips said.